Hypothesis test of Spearman’s rank correlation coefficien
A researcher claims that, at a river bend, the water gradually gets deeper as the distance from the inner bank increases. He measures the distance from the inner bank, \(b \mathrm {~cm}\), and the depth of a river, \(s \mathrm {~cm}\), at seven positions. The results are shown in the table below.
Position
\(A\)
\(B\)
\(C\)
\(D\)
\(E\)
\(F\)
\(G\)
Distance from
inner bank \(b \mathrm {~cm}\)
100
200
300
400
500
600
700
Depth
\(s \mathrm {~cm}\)
60
75
85
76
110
120
104
Calculate Spearman's rank correlation coefficient between \(b\) and \(s\).
Stating your hypotheses clearly, test whether or not the data provides support for the researcher's claim. Use a \(1 \%\) level of significance.